No. Reviewsion does not extend or restart a paid trial. Each plan's 14-day trial is given once per shop.
You can stay on the Free plan for nothing. If you haven't used the other paid plan's trial, it is still available. If you partly used a plan's trial, only its unused days are available when you return. Reinstalling does not restart a used trial.
To check your days, open Settings, then Account and Billing, and view the plans. Each paid plan shows its available trial days before you approve it.
Installed before ? Your 30-day trial continues until it ends; then choose Free, Standard or Pro. Starting a Standard or Pro trial before then ends the 30-day trial, and its remaining days don't carry over.